1 Lecture 8: Financing Based on Book Values Discounted Cash Flow, Section 2.5 © 2004, Lutz Kruschwitz and Andreas Löffler

The problem WACC is one of the most popular methods of evaluating a firm. But: it requires a deterministic leverage to market values, or  if share price goes up  debt has to go up as well and  if share price goes down  debt goes down as well and  if share price goes up/down  debt goes up/down as well. This assumption seems very unrealistic. But what happens with the valuation formula if we replace the market values by book values? That is the aim of this section!

The assumptions Let us talk about book values. We assume for the book value of debt and no default or But that does not make sense with equity: usually What drives the book value of equity?

Book value of equity What influences book value of equity Three elements are possible: 1.Increase of subscribed capital (which we assume to be zero). 2.Retained earnings after tax given by 3.Paid dividends given by cash flows to shareholders, or

Clean surplus relation Hence, the book value of equity has to satisfy which can be simplified to Assumption 2.17 (clean surplus relation) This leads to our next theorem.

Operating assets relation Theorem 2.13 (operating assets relation): The book value of the firm follows This relation invokes elements from the levered as well as from the unlevered firm. Since cash flows and EBIT are random, the book value will be a random variable as well.

Financing based on book values Definition 2.9 (financing based on book values): A company is financed based on book values if debt ratios to book values are deterministic. To get an idea of the company‘s value more information necessary: we need to know about investment and accruals since they drive the book value.

Investment and accruals Hence,

Investment and accruals Hence,

Investment policies The rhs of (2.21) depends on the investment policy and accruals Now three investment policies are differentiated: 1.Investment due to full distribution; 2.replacement investments; 3.investment based on cash flows.

Full distribution policy The profit after interest and taxes is Owners receive In case of a full distribution policy both amounts are identical. Hence, Definition 2.10 (full distribution policy): A levered firm carries out a full distribution policy if

Remarks It is doubtful whether full distribution is a realistic behaviour, but it has a strong tradition in Germany. It is equivalent to investments completely financed by debt: And it implies that book value of equity stays constant:

Valuation The last equation implies: the book value of equity is deterministic. But if the leverage ratio is deterministic as well, debt is deterministic: Then the adjusted present value approach is appropriate: Theorem 2.14 (full distrubution): If the firm is financed based on book values and carries out full distribution, then Proof: immediate.

Replacement investment Definition 2.11 (replacement investment): A firm takes on replacement investments if for all t Then Hence, there is no difference between profits and cash flows of the unlevered firm. Hence, using the operating liabilities relation

Valuation The last equation implies: the book value of the firm is deterministic. But if the leverage ratio is deterministic as well, debt is deterministic Then the adjusted present value approach is appropriate. Theorem 2.15 (replacement investment): If the firm is financed based on book values and carries out replacement investment, then Proof: immediate.

Investment based on cash flows Now let us turn to a more realistiv case - investments are tied to cash flows: -increasing cash flows raise investments, -decreasing cash flows lower investments. Investments are aligned with the unlevered firm (investments are independent of leverage!), or

Gross cash flows and investment To motivate our assumption let us look at gross cash flows. They are paid to and for 1. tax authority, 2. investments, and 3. shareholder and creditors. If investments get a fixed portion, it should depend on gross cash flow after taxes But this implies our assumption since (see (2.22))

Accruals Assumption 2.9 (no discretionary accruals): Accruals follow for all t It is necessary that past investments Inv -1 to Inv -n+1 must be known. Our assumption is certainly satisfied if depreciation is the only element of accruals and if we apply straight-line depreciation.

Valuation Given all assumptions a valuation theorem can be verified (see Theorem 2.17). Unfortunately, this formula is very muddled... Important drivers for value are: 1.tax rate, riskless interest rate ( , i.e. market value increases with them), cost of capital ( , i.e. value decreases with them); 2.today´s book value (  ), past investments (  ); 3.leverage ratio to book values (  ); 4.investment ratio a (  ); 5.depreciation period n (~  ) - requires explanation.

Market value and depreciation If accruals (depreciation) increase Þ(given the investment!) book values increase Þ (given the leverage ratio) debt increases Þ tax advantages increase Þ market values increase.

Long-term constant debt ratios A simpler formula can be obtained for infinite horizon. We assume -an infinite lifetime -a constant debt ratio and a constant investment parameter α, and -disregard past investments. Then (Theorem 2.18) This formula looks very like Modigliani-Miller, except for the term in brackets!

Infinite example We use No investments before t = 0. Then (Remark: Here we use the approximation formula)

23 Summary Financing based on book values requires knowledge of the investment policy. The operating liabilities relation reveals movement of book values. Three investment policies can be considered: -full distrubition (or debt financed investments)  APV; -replacement investments  APV; -investments based on cash flows  MoMi-like formula.